应用数学力学方法研究沥青路面结构特性
|
摘要
本文应用数学力学方法，分析了沥青路面结构在三种状态下的性能，即常温下的一般受力状态、高温下的粘弹性能和低温下的抗开裂性能。
对于常温状态下的沥青路面结构，利用弹性层状体系理论，分析了层状路基合成模量的计算方法，得到了双层弹性层状弹性体系当量模量诺模图，并分析了当量模量的影响参数。对柔性承载板、刚性承载板作用下的当量模量，以及规范上的当量模量计算公式进行了对比，发现三种情况的差异较大，特别是规范上的计算公式甚至有得到负值模量的情况，严重与实际不符。
分析了长寿命路面结构的概念和含义，以及设计指标的合理选取。对两种长寿命路面的结构形式进行了参数分析，得到了设计指标最为敏感的影响参数，为陕蒙路提出了试验路方案和推荐型式。提出了路面结构和造价的优化规划方法，对规定参数范围和设计指标的一个例子进行了优选，根据各结构层的造价函数，对目标函数为造价的规划进行了计算。
根据对应原理，求解了粘弹性半空间体，对其表面位移进行了参数分析，发现对不可回复粘性系数最为敏感，而对可回复弹性和粘性系数最不敏感。通过拉普拉斯逆变换的数值法，求解了粘弹性双层体系，总结了利用对应原理和拉普拉斯逆变换数值方法求解多层体系的一般方法。以三层体系的沥青路面为例，为沥青面层提出了三种不同的非线性粘弹性模型，以考虑沥青面层随着荷载次数增加的固结效应。提出了车辙的计算方法，计算了车辙与荷载作用次数的关系，分析了车辙的各种影响因素。
对于路面材料的抗开裂性能，分析比较了各种评价试验方法，着重对SCB试件进行了分析，利用有限元方法计算SCB试件裂尖附近的应力和位移分布，根据断裂力学理论求得了不同裂缝长度时的应力强度因子，拟合了计算公式，讨论了其影响因素。对路面结构的芯样和试验室的两种试件进行了SCB试验，得到了它们0℃和-20℃下的断裂韧度。对于路面结构的反射裂缝和自上而下裂缝，建立了有限元分析模型，分析计算了它们在5℃、20℃下Ⅰ型、Ⅱ型开裂的应力强度因子，拟合了计算公式，对四种面层厚度不同的情况进行了对比，分析了不同面层模量对应力强度因子的影响。利用描述裂缝扩展速率的Paris公式分析了Ⅰ型开裂裂缝的寿命，得到了裂缝长度与荷载作用次数的关系曲线，对不同面层厚度、不同裂缝类型的寿命进行了比较。
In this paper,the performance of asphalt pavement under the condition of ambientternperature,high temperature and low temperature was analyzed by the methods ofmathematics and mechanics.
According to the elastic layers system theory,the equivalent elastic modulus oflayed-foundation of asphalt pavements under ambient temperature was formulated andcalculated,and the parameters influencing it were analyzed.The comparision of equivalentelastic modula under flexible and rigid bearing plate and got by the specification showed thethree methods were difference each other very much,especially the method in thespecification existed a fatal error that it can lead the modulus to be a negative,which wasimpossible in fact.
This paper discussed the idea and signification of long-life pavement and its design target.The structures of two kinds of long-life pavements were analyzed,and the most sensitiveparameters of its design target.Based on the analysis,four kinds of test road structure wereproposed for the Shan-Meng highway.Optimizing methods of pavements structure and roadcost were used to analyze the long-life pavements.
The visco-elastic half space was solved according to the correspondence principle,andthe influencing parameters of surface displacement were analyzed;the results indicated thatthe surface displacement's most sensitve parameter was the inrecoverable viscocitycoefficient,and the two insensitive paramenters were the recoverable elasticity coefficientand recoverable viscocity coefficient.The two-layer visco-elastic system was solved by thenumerical inversion of Laplace transform,and the general solution of multilayeredvisco-elastic system was concluded.Taking the three-layer visco-elastic asphalt pavement asan example,three nonlinear visco-elastic models were introduced to consider the asphaltlayer's consolidation with the increasing of load times.A computing method of rut wasproposed to analyze the relation between the rut and load times,and the influence factorswere also studied.
As for the anti-crack performance of asphalt concrete,several test methods werediscussed and the emphase was put on the SCB(Semi-Circular Bending)specimen.The stress intensity factors of the cracks in SCB specimen were calculated by the fracturemechanics theory and FEM(Finite Element Method);its fiting formula was got and itsinfluence factors were discussed.The SCB specimens from pavements and laboratory weretested at 0℃and-20℃,and their fracture toughnesses were got.As for the reflective crackand top-to-down crack in the asphalt pavements,FEM models were constructed for them,andtheir stress intensity factors at 5℃and 20℃were calculated and fitted.The results of fourthicknesses of asphalt layer were analyzed and compared,and the effects of asphalt layermodulus on crack's stress intensity factor were discussed.Using the Paris law,the relationbetween load times and crack length forⅠtype cracking was obtained,and the lifes ofreflective cracks and top-to-down cracks in asphalt layer with different thickness wereanalyzed.
对于常温状态下的沥青路面结构，利用弹性层状体系理论，分析了层状路基合成模量的计算方法，得到了双层弹性层状弹性体系当量模量诺模图，并分析了当量模量的影响参数。对柔性承载板、刚性承载板作用下的当量模量，以及规范上的当量模量计算公式进行了对比，发现三种情况的差异较大，特别是规范上的计算公式甚至有得到负值模量的情况，严重与实际不符。
分析了长寿命路面结构的概念和含义，以及设计指标的合理选取。对两种长寿命路面的结构形式进行了参数分析，得到了设计指标最为敏感的影响参数，为陕蒙路提出了试验路方案和推荐型式。提出了路面结构和造价的优化规划方法，对规定参数范围和设计指标的一个例子进行了优选，根据各结构层的造价函数，对目标函数为造价的规划进行了计算。
根据对应原理，求解了粘弹性半空间体，对其表面位移进行了参数分析，发现对不可回复粘性系数最为敏感，而对可回复弹性和粘性系数最不敏感。通过拉普拉斯逆变换的数值法，求解了粘弹性双层体系，总结了利用对应原理和拉普拉斯逆变换数值方法求解多层体系的一般方法。以三层体系的沥青路面为例，为沥青面层提出了三种不同的非线性粘弹性模型，以考虑沥青面层随着荷载次数增加的固结效应。提出了车辙的计算方法，计算了车辙与荷载作用次数的关系，分析了车辙的各种影响因素。
对于路面材料的抗开裂性能，分析比较了各种评价试验方法，着重对SCB试件进行了分析，利用有限元方法计算SCB试件裂尖附近的应力和位移分布，根据断裂力学理论求得了不同裂缝长度时的应力强度因子，拟合了计算公式，讨论了其影响因素。对路面结构的芯样和试验室的两种试件进行了SCB试验，得到了它们0℃和-20℃下的断裂韧度。对于路面结构的反射裂缝和自上而下裂缝，建立了有限元分析模型，分析计算了它们在5℃、20℃下Ⅰ型、Ⅱ型开裂的应力强度因子，拟合了计算公式，对四种面层厚度不同的情况进行了对比，分析了不同面层模量对应力强度因子的影响。利用描述裂缝扩展速率的Paris公式分析了Ⅰ型开裂裂缝的寿命，得到了裂缝长度与荷载作用次数的关系曲线，对不同面层厚度、不同裂缝类型的寿命进行了比较。
In this paper,the performance of asphalt pavement under the condition of ambientternperature,high temperature and low temperature was analyzed by the methods ofmathematics and mechanics.
According to the elastic layers system theory,the equivalent elastic modulus oflayed-foundation of asphalt pavements under ambient temperature was formulated andcalculated,and the parameters influencing it were analyzed.The comparision of equivalentelastic modula under flexible and rigid bearing plate and got by the specification showed thethree methods were difference each other very much,especially the method in thespecification existed a fatal error that it can lead the modulus to be a negative,which wasimpossible in fact.
This paper discussed the idea and signification of long-life pavement and its design target.The structures of two kinds of long-life pavements were analyzed,and the most sensitiveparameters of its design target.Based on the analysis,four kinds of test road structure wereproposed for the Shan-Meng highway.Optimizing methods of pavements structure and roadcost were used to analyze the long-life pavements.
The visco-elastic half space was solved according to the correspondence principle,andthe influencing parameters of surface displacement were analyzed;the results indicated thatthe surface displacement's most sensitve parameter was the inrecoverable viscocitycoefficient,and the two insensitive paramenters were the recoverable elasticity coefficientand recoverable viscocity coefficient.The two-layer visco-elastic system was solved by thenumerical inversion of Laplace transform,and the general solution of multilayeredvisco-elastic system was concluded.Taking the three-layer visco-elastic asphalt pavement asan example,three nonlinear visco-elastic models were introduced to consider the asphaltlayer's consolidation with the increasing of load times.A computing method of rut wasproposed to analyze the relation between the rut and load times,and the influence factorswere also studied.
As for the anti-crack performance of asphalt concrete,several test methods werediscussed and the emphase was put on the SCB(Semi-Circular Bending)specimen.The stress intensity factors of the cracks in SCB specimen were calculated by the fracturemechanics theory and FEM(Finite Element Method);its fiting formula was got and itsinfluence factors were discussed.The SCB specimens from pavements and laboratory weretested at 0℃and-20℃,and their fracture toughnesses were got.As for the reflective crackand top-to-down crack in the asphalt pavements,FEM models were constructed for them,andtheir stress intensity factors at 5℃and 20℃were calculated and fitted.The results of fourthicknesses of asphalt layer were analyzed and compared,and the effects of asphalt layermodulus on crack's stress intensity factor were discussed.Using the Paris law,the relationbetween load times and crack length forⅠtype cracking was obtained,and the lifes ofreflective cracks and top-to-down cracks in asphalt layer with different thickness wereanalyzed.
引文
[1]郑传超，王秉纲．道路结构力学计算[M]．北京：人民交通出版社．2002
[2]Y.H.Huang.Stress and Displacement in viscoelastic Layered System Under Circular Loaded Areas”,2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V1,170-188.
[3]J.E.Ashton.Analysis of Stress and Displacement in Three-layer Viscoelastic Systems.2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V 1,147-162.
[4]Kenji Ishihara.The Theory of Viscoelastic Two-layer Systems and the Conception of its Application to the Pavement Design.2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V1,147-162
[5]严作人．粘弹性半空间体的力学分析[J]．同济大学学报，1987，2
[6]严作人．粘弹性层状体系的力学分析[J]．同济大学学报．1988，16(4)：473-483
[7]徐远杰．半空间Burgers粘弹性体受集中力的理论解[J]．武汉水利电力大学学报．1997，30(2)，37-41
[8]任瑞波、钟阳、谭忆秋、张肖宁．多层粘弹性半空间轴对称问题的理论解[J]．哈尔滨建筑大学学报．2000，33(6)，124-128
[9]任瑞波、谭忆秋、张肖宁．FWD动荷载作用下沥青路面层状体粘弹解与弹性解分析[J]．中国公路学报．2001，14(2)，9-17
[10]任瑞波、谭忆秋、张肖宁．FWD动荷载作用下沥青路面层状体粘弹解与弹性解分析[J]．哈尔滨建筑大学学报．2001．34(5)，116-120
[11]任瑞波、钟岱辉、孔军、田军祯、董支宝、李兵．沥青路面层状粘弹性半空间轴对称问题的求解[J]．山东建筑工程学报．2002，17(4)，1-7
[12]钟阳，陈静云，王龙，李玉华．求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法[J]．计算力学学报．2003，20(6)：749-755
[13]任瑞波、谭忆秋、钟岱辉．沥青路面粘弹性问题的理论分析[J]．四川建筑科学研究．2004，30(1)，76-79
[14]郭大智、任瑞波．层状粘弹性体系力学[M]．哈尔滨工业大学出版社．2001，哈尔滨
[15]朱永灵．沥青路面的车辙研究[D]：[硕士学位论文]．上海：同济大学道路与交通工程，1988
[16]许志鸿，郭大智，吴晋伟等．沥青路面车辙的理论计算[J]．中国公路学报．1990．3(3)：27-36
[17]徐世法．沥青路面的粘弹性力学分析与车辙预估[D]：[硕士学位论文]．上海：同济大学道路与交通工程，1988
[18]徐世法．高等级道路沥青路面车辙预估和防治[D]：[博士学位论文]．上海：同济大学道路与交通工程，1991
[19]李一鸣，俞建荣．沥青路面车辙形成机理力学分析[J]．东南大学学报，1994，14(1)：90-95
[20]黄晓明，张晓冰，邓学钧．沥青路面车辙形成规律环道试验研究[J]．东南大学学报，2000，30(5)：96-101
[21]张登良，李俊．高等级道路沥青路面车辙研究[J]．中国公路学报，1995，8(1)
[22]郝培文，吴微，张登良．不同沥青用量与级配组成对沥青混合料抗车辙性能的影响[J]．西安公路交通大学学报．1998(3)：199-202
[23]Fenella Margaret Long.Permanent Deformation of Asphalt Concrete pavements:A Nonlinear Viscoelastic Approach to Mix Analyses and Design.Papers for doctor degree,University of californla,berkele USA,2001.2632
[24]Model Prediction of Rutting in Asphalt Concrete.Journal of Transportation Engineering. September/October 1998: 448-456
[25] Jacob Uzan. Permanent Deformation in Felxible Pavements. Journal of Transportation Engineering.January/Februar 2004: 6-13
[26] A.C. Collop. A Visco-Elastic Approach to Rutting in Felxible Pavements. CUED/C-MECH/TU 49.September 1992.
[27] Kamil Elias Kaloush. Simple Performance Test for Permanent Deformation of Asphalt Mixture.Papers for Doctor Degree Arizona State University, USA, 2001
[28] Sousa J B, Deacon J A, Weissman S L, etc. Permanent Deformation of Aggregate Mixes[R].Washington D C: Strategic Highway Research Program, National Research Program Council, Report NO. SHRP-415, 1994
[29] Chen J S ,Tsai C J. How Good are Linear Viscoealstic Properties of Aspalt Binder to Predict Rutting and Fatigue Craking? Journal of Material and Performance, 1999,8(4): 443-449
[30] Weissman, S L, Sackman J, Harvey J T,et al. Seledtion of Laboratory Test Specimen Dimension for Permanent Deformation of Aspalt Concrete Pavements. Transportation Research Record 1681, 1999:113-120
[31] Fujie Zhou,Tom Scullion. DiscussiomThree Stages of Permanent Deformation Curve and Ruting Model. The Internationa] Journal of Pavement Engineering. Uol. 3(4). 2002, P251-260
[32] R.A.Tarefder,M.Zaman,K,Hobason.A Laboratory and Statistical Evaluantion of Factors Affecting Rutting.The International journal of Pavement Engineering.Vol.4(1) March 2003, P59-68
[33] Kandhal, P S, R B Mallick. Effects of gradation on Rutting Potential of Dense Graded Asphalt Mixtures. TRB, No 1767, 2001, P146-151
[34] Elie Y Hajj, Raj V Siddliartlian, et al. Development of Laboratory Based Uufied Permanent Deformation Model of HMA Mixture [C]. 84th TRB Annual Meeting January 9-13, 2005
[35] Cluadc Villicrs ct al. Intcrprctationg of Transverse Profiles to Detemine the Source of Rutting within Asphalt Pavement system[C]. 84th TRB Annual Meeting January 9-13, 2005
[36] Jorge B. Sousa, Joseph Craus, Carl L. Monismith. Summary Report on Permanent Deformation in Asphalt Concrete (SHRP-A/IR-91 -104). Strategic Highway Research Program. National Research Council. Washington, D, C. 1991
[37] Griffith A A. The phenomena of rupture and flow in solids. Phil.Trans. Roy. Soc. 1921, A211 163
[38] Irwin G R. Fracture Dynamics in Fracturing of Metals. ASTM Cleveland, 1948
[39] Irwin G R. Analysis of Stresses and Strains near the end of a crack traversing a plane. J Appl Mech.1957,24:361
[40] Mushkelishivili N I. Some Basic Problems of the Mathematical Theory of Elasticity. Translated by J R M Radok Noordhoff, 1963
[41] Dugdale D S.Yielding of steel sheets containing slits. J Mech. Phys Solids. 1960, 8: 100-104
[42] Wells A A. Unstable crack propagation in metals: Cleavage and Fast Fracture, Crack Propagation Symposium, Cranfield, 1961
[43] Billby B A, Cottrell A H and Swinden K H. The Spread of plastic yield from a notch Proc. Roy Soc 1964,A272 304
[44] Rice J R. A path independent integral and the approximate analysis of strain concentration by nothces and cracks[J]. Appl Mech. 1968, 379-385
[45] Sih G C. A special theory of crack propagation in Mechanics of Fracture (G C Sih ed) Vol. 1 Noordhoff, 1973
[46] Kaplan M F. Crack propagation and the fracture of concrete. J Am. Concrete Inst. 1961, 58: 591-610
[47]Bazant ZP and Oh,B.H.Crack band theory for facture of concrete[J].Materials and Structures,1983,16(93):155～177
[48]胡庆安，程侠，邰卫华．金属材料断裂预测损伤破坏准则的应用．长安大学学报(自然科学版)：2007，27(4)：100～102
[49]李雪红，徐洪钟，顾冲时．水工混凝土结构裂缝的稳定性分析．南京工业大学学报：2007，29(3)：20～24
[50]Jayatilaka des Ayal.Fracture of Engineering Brittle Materials[M].England,1979
[51]Elin A.Jensen,Will Hansen.Fracture Energy Test for Highway Concrete.Transportation Research Record 1730 Paper No.00-0937
[52]R.L.Krans,E.Tolman,M.F.C.Van De Ven.Semi-circular bending test:a practical crack growth test using asphalt concrete cores.Reflective Cracking in Pavements.Edited by L.Francken,E,Beuving and A.A.A.Molenaar.(?)1996 RILEM.Published by E & FN Spon,2-6 Bounary Row,London,SEI 8HN.ISBN 0 419 22260 X
[53]E.K.Tschegg,S.E.Tschegg-stanzl,J.Litzka.Fracture behaviour and bond strength of bituminous layers.Reflective Cracking in Pavements.Edited by L.Francken,E,Beuving and A.A.A.Molenaar.(?)1996 RILEM.Published by E & FN Spon,2-6 Bounary Row,London,SEI 8HN.ISBN 0 419 22260 X
[54]Mihai O.Marasteanu,Xue Li,Joseph E Labuz.Cracking in Pavements-Mitigation Risk Assessment and Prevention,5th International RILEM Conference,Limoges,France,5-7 May 2004
[55]J.M.Read.New Method for Measuring Crack Propagation in Asphalt Concrete[J].International Journal for Pavement Engineering.Vol:1 No.1 pp 15-35.2000
[56]K.W.Kim,H.M.E Hussein.Effect of Differential Contraction on Fracture Tougness of Asphalt Material at Low Temperatures[J].AAPT.1995
[57]Zhiwang Zhang,Reynaldo Roque,and Bjorn Birgisson.Evalution of Laboratory-Measured Crack Growth Rate for Asphalt Mixtures.Transportation Research Record 1767 paper No.01-0272.2001
[58]Aysar NAJD、郑传超．测量加筋沥青混凝土内的裂缝扩展(英文)．Journal of Southeast University(东南大学学报：英文版)2005．21(3)：342-347
[59]Aysar NAJD、郑传超、郭进英．纤维加筋沥青混凝土断裂性能试验．长安大学学报：自然科学版—2005．25(3)：28-32
[60]Aysar NAJD、郑传超．利用玻璃纤维增加沥青混凝土的断裂潜能研究．西安工业学院学报，2005年第02期：169-173
[61]张登良．半刚性基层沥青路面地断裂力学计算方法及其应用．中国公路学报，1998．11(2)：30-38
[62]孙立军．复合路面荷载型反射裂缝的力学分析和试验路验证．土木工程学报，2005．35(1)：50-56
[63]彭妙娟、程玉民．西三线沥青路面的荷载应力和温度应力分析．西安理工大学学报，1998年第二期
[64]杨春风．基层含裂缝沥青路面的应力分析．黑龙江工程学院学报．2003．17(3)：9-11
[65]杨春风．半刚性基层沥青路面温缩裂缝的有限元分析．桂林工学院学报．2004．24(1)：52-54
[66]毛成、邱延峻、李云鹏沥青路面表面裂纹扩展模拟及影响因素分析．西南交通大学学报．2004．39(4)：437-441
[67]杨春风．断裂力学理论在道路疲劳寿命预测中的应用．昆明理工大学学报．2003．28(6)：87-90
[68]贾艳东、宋玉普、黄志强．测定混凝土断裂参数试验方法的研究．低温建筑技术．2004(2)：11-13
[69]曾梦澜、马正军、易昕．广义Paris公式预测沥青路面的疲劳寿命．湖南大学学报(自然科学版)，2005年06期
[70]Seo Y,Kim YR,Schapery RA,Witczak MW,Bonaquist R.A study of crack-tip deformation and crack growth in asphalt concrete using fracture mechanics.Journal of the Association of Asphalt Paving Technologists.Volume:73 Conference Title:Technical Sessions of the Journal of the Association of Asphalt Paving Technologists.2004 Proceedings.Location:Baton Rouge,Louisiana
[71]Brooker T,Foulkers MD,Kennedy CK.Influence of mix design on reflection cracking growth rates through asphalt surfacing.Sixth international conference,structural design of asphalt pavements,volume I,proceedings,university of michigan,july 13-17,1987,ANN ARBOR,Michigan
[72]Majidzadeh K,Kauffmann EM,Chang CW.Verification of fracture mechanics concepts to predictcracking of flexible pavements
[73]Majidzadeh Kamran,Kauffmann E.M,Saraf C.L.Analysis of fatigue of paving mixtures from the fracture mechanics viewpoint
[74]F.Durbin(1974),Numerical inversion of Laplace transforms:an efficient improvement to Dubner and Abate's method[J],The Computer Journal,V.17.No.4,pp.371-376
[75]Dubner,R.,and Abate,J.(1968).Numerical inversion of Laplace transforms by relating them to the finite Fourier Cosine transform,J.ACM,Vol.15,No.1,pp.115-123
[76]S.Crump,Numerical inversion of Laplace transforms using a Fourier series approximation,JACM.,23(1976),89-96
[77]M.K.Miller and T.W.Guy,Numerical inversion of the Laplace transform by use of Jacobi polynomisls,SIAM Journal of Numerical Analysis,Vol.,3,624-635(1966)
[78]Davis,B 和 Martin,B.,Numerical Inversion of the Laplace Transform:ASurvey and Comparison of Methods,J.Comput.Phys.33(1979),1-32
[79]戴煜．Laplace变换的代数数值反演方法．数值计算与计算机应用．2001，No．4，281-285
[80]单华宁．Laplace变换的数值反演方法的研究．数值计算与计算机应用．1999，No．3：231-236
[81]谢咏梅，胡娟，单华宁，王国清．Laplace变换的数值反演算法的研究．南京师大学报(自然科学版)．Vol．24，No．4(2001)：12-15
[82]范天佑．断裂理论基础．科学出版社．2002年，北京
[83]郑传超．道路结构断裂力学基础[M]．西安：西北工业大学出版社．1997年11月。
[84]陈小庭，孙立军，李峰．长寿命沥青混凝土路面结构特点与设计研究．公路．2005年8月，第8期
[85]JTJ 014-97．沥青路面设计规范[S]．北京：人民交通出版社
[86]邓学钧．路基路面工程[M]．北京：人民交通出版社．2000
[87]徐世法．高等级道路沥青路面车辙的预估控制与防治．同济大学博士学位论文．1991．12
[88]任瑞波，谭忆秋，钟岱辉．沥青路面粘弹性问题的理论分析．四川建筑科学研究．第30卷，第1期，2004年3月
[89]任瑞波，钟阳，张肖宁，郭大智．多层粘弹性半空间地基对称问题的理论解．哈尔滨建筑大学学报．第33卷，第6期，2000年12月
[90]钟阳，陈静云，王龙，李玉华．求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法．计算力学学报．第20卷，第6期，2003年12月
[91]郑健龙，关宏信．温缩型反射裂缝的热粘弹性有限元分析．中国公路学报．第14卷，第3期，2001年7月
[92]任瑞波，谭忆秋，张肖宁．FWD动荷载作用下沥青路面层状体系粘弹解与弹性解分析．哈尔滨建筑大学学报．第34卷，第5期，2001年10月
[93]R.L.Krans et al.Semi-circular bending test:a practical cracks growth test using asphalt concrete cores
[94]R.L Krans,F.Tohnan and M.F.C.Van De Ven.Semi-Circular Bending test Using Core.[C]The Third International Conference on Reflective Cracking in Pavement,Maastricht,The Netherlands.1996
[95]Ye Guozheng.Fatigue Shear and Fracture Behavior of Rubber Bituminous Pavement[C].Third International Conference on Reflective Cracking in Pavements.1996
[96]沙庆林．高等级公路半刚性基层沥青路面[M]．北京：人民交通出版社．1999
[97]郝培文等．沥青混合料低温抗裂性能评价指标．西安公路交通大学学报，第20卷，第3期．2000
[98]F.J.Zhou and Sun Lijun.Lab Asphalt Testing Evaluation of Reflective Cracking[C].Accelerated Pavement Testing International Conference,Reno,Nevada 1999
[99]F.J.Zhou.Anti-Reflective Cracking Measures and Mechanistic Analysis[D].Ph.D.Dissertation,Tongji University.1998
[100]周志刚，张起森．加筋材料阻止沥青路面反射裂缝的桥联增韧的有限元分析．土木工程学报．Vol．33(1)：93-99(2000)
[101]易志坚，吴国雄．基于断裂力学原理的水泥混凝土路面破坏过程分析及路而设计新构想．重庆交通学院学报．Vol．2(1)：1—5(2001)
[102]罗睿，黄晓明．利用权函数计算沥青路面层间部分约束的面层底裂缝应力强度因子．岩土工程学报．Vol．23(5)：610-613(2001)
[103]才华，张敏江．反射裂缝的断裂及疲劳分析和模拟计算．沈阳建筑工程学院学报．Vol．13(3)：252-258(1997)
[104]冯建亚．沥青混凝土罩面层的开裂破坏规律分析．硕士毕业论文．大连理工大学，2002
[105]焦新海，周行春．半刚性路面反射裂缝防治措施研究综述．重庆交通学院学报．Vol．17(1)：52-57(1998)
[106]郑健龙，张起森．半刚性路面反射裂缝及其应力强度因子的有限元分析．岩土工程学报．1990，12(3)：22-26
[107]罗睿，黄晓明．沥青路面表面裂缝应力强度因子计算方法研究．公路交通科技，2002，19(1)：13-15
[108]彭妙娟，张登良，夏永旭．半刚性基层沥青路面的断裂力学计算方法及其应用．中国公路学报．1998，11(2)：30-38
[109]刘益河，张起森．用热光弹法研究路面裂缝稳定性问题．实验力学，1992，7(4)：364-370
[110]刘益河，张起森．用温度光弹法确定路面结构裂缝的应力强度因子．长沙交通学院学报．1991，7(1)．71-80
[111]M.A.Caltabianl and J.M.Brunton.Reflection Cracking in Asphalt Concrete[J].A.A.P.T,Vol 60,pp310-3320.1991
[112]Majidzadeh.Improved Methods to Eliminate Reflection Cracking,Report FHWA/RD-86/07,Washington,D.C.1985
[113]C.L.Monismith.Reflection Cracking:Analysis,Laboratory Studies,and Design Consideration[J].AAPT,Vol.49.1980
[114]S.J.Sulaiman,A.F.Stock.The Use of Fracutre Mechanics for The Evaluation of Asphalt Mixes.[C].AAPT.1995
[115]M.M.Jacobs,P.C.Hopman,A.A.A.Moleneer.Application of Fracture Mechanics Principle to Analyze Cracking in Asphalt Concrete[J].AAPT,Vol 65,1996
[116]Fatigue Response of Asphalt Aggregate Mixes Asphalt Research Program.Institute of Transportation Studies,SHRP,National Research Council,University of California,Berkeley,Washington,66 DC 1994
[117]Yoon-Ho Cho,Chiu Liu,Terry Dossey,et al.Asphalt Overlay Design Methods for Rigid Pavements Considering Rutting,Reflection Cracking and Fatigue Cracking Research Report 987-9,Center for Transportation Research Bureau of Engineering Research.University of Texas,Austun.1998
[118]R.A.A.Schapery.Theory of Crack Growth in Visco-Elastic Media,Report MM 2764-73-1,Mechanics and Materials Research Centre,Texas&M University,Texas.1973
[119]A.A.A Molenaar and Snods.Design Methods for Plain and Geogrid Reinforced Overlay[C].The third International Conference on Reflective Cracking in Pavements.1996
[120]A.Scarpas.Finite Elements Modeling of Cracking in Pavements[C].Third International Conference on Reflective Cracking in Pavements,Maastricht,The Netherlands.1996
[121]A.Scarpas,Blaauwendraad J,A.H.De Bondt and A.A.A.Molenaar.CAPA:A Modern Tool for The Analysis and Design of Pavements.[C].Second International RILEM Conference on Reflective Cracking in Pavements,Liege.1993
[122]张妍．沥青混凝土路面病害与加铺层的力学分析．长安大学硕士学位论文．2005年5月
[123]陈玉，沥青路面低温缩裂分析．长安大学硕士论文．2006年5月
[2]Y.H.Huang.Stress and Displacement in viscoelastic Layered System Under Circular Loaded Areas”,2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V1,170-188.
[3]J.E.Ashton.Analysis of Stress and Displacement in Three-layer Viscoelastic Systems.2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V 1,147-162.
[4]Kenji Ishihara.The Theory of Viscoelastic Two-layer Systems and the Conception of its Application to the Pavement Design.2nd International Conference on the Structureal Design of Asphalt Pavements.1967,V1,147-162
[5]严作人．粘弹性半空间体的力学分析[J]．同济大学学报，1987，2
[6]严作人．粘弹性层状体系的力学分析[J]．同济大学学报．1988，16(4)：473-483
[7]徐远杰．半空间Burgers粘弹性体受集中力的理论解[J]．武汉水利电力大学学报．1997，30(2)，37-41
[8]任瑞波、钟阳、谭忆秋、张肖宁．多层粘弹性半空间轴对称问题的理论解[J]．哈尔滨建筑大学学报．2000，33(6)，124-128
[9]任瑞波、谭忆秋、张肖宁．FWD动荷载作用下沥青路面层状体粘弹解与弹性解分析[J]．中国公路学报．2001，14(2)，9-17
[10]任瑞波、谭忆秋、张肖宁．FWD动荷载作用下沥青路面层状体粘弹解与弹性解分析[J]．哈尔滨建筑大学学报．2001．34(5)，116-120
[11]任瑞波、钟岱辉、孔军、田军祯、董支宝、李兵．沥青路面层状粘弹性半空间轴对称问题的求解[J]．山东建筑工程学报．2002，17(4)，1-7
[12]钟阳，陈静云，王龙，李玉华．求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法[J]．计算力学学报．2003，20(6)：749-755
[13]任瑞波、谭忆秋、钟岱辉．沥青路面粘弹性问题的理论分析[J]．四川建筑科学研究．2004，30(1)，76-79
[14]郭大智、任瑞波．层状粘弹性体系力学[M]．哈尔滨工业大学出版社．2001，哈尔滨
[15]朱永灵．沥青路面的车辙研究[D]：[硕士学位论文]．上海：同济大学道路与交通工程，1988
[16]许志鸿，郭大智，吴晋伟等．沥青路面车辙的理论计算[J]．中国公路学报．1990．3(3)：27-36
[17]徐世法．沥青路面的粘弹性力学分析与车辙预估[D]：[硕士学位论文]．上海：同济大学道路与交通工程，1988
[18]徐世法．高等级道路沥青路面车辙预估和防治[D]：[博士学位论文]．上海：同济大学道路与交通工程，1991
[19]李一鸣，俞建荣．沥青路面车辙形成机理力学分析[J]．东南大学学报，1994，14(1)：90-95
[20]黄晓明，张晓冰，邓学钧．沥青路面车辙形成规律环道试验研究[J]．东南大学学报，2000，30(5)：96-101
[21]张登良，李俊．高等级道路沥青路面车辙研究[J]．中国公路学报，1995，8(1)
[22]郝培文，吴微，张登良．不同沥青用量与级配组成对沥青混合料抗车辙性能的影响[J]．西安公路交通大学学报．1998(3)：199-202
[23]Fenella Margaret Long.Permanent Deformation of Asphalt Concrete pavements:A Nonlinear Viscoelastic Approach to Mix Analyses and Design.Papers for doctor degree,University of californla,berkele USA,2001.2632
[24]Model Prediction of Rutting in Asphalt Concrete.Journal of Transportation Engineering. September/October 1998: 448-456
[25] Jacob Uzan. Permanent Deformation in Felxible Pavements. Journal of Transportation Engineering.January/Februar 2004: 6-13
[26] A.C. Collop. A Visco-Elastic Approach to Rutting in Felxible Pavements. CUED/C-MECH/TU 49.September 1992.
[27] Kamil Elias Kaloush. Simple Performance Test for Permanent Deformation of Asphalt Mixture.Papers for Doctor Degree Arizona State University, USA, 2001
[28] Sousa J B, Deacon J A, Weissman S L, etc. Permanent Deformation of Aggregate Mixes[R].Washington D C: Strategic Highway Research Program, National Research Program Council, Report NO. SHRP-415, 1994
[29] Chen J S ,Tsai C J. How Good are Linear Viscoealstic Properties of Aspalt Binder to Predict Rutting and Fatigue Craking? Journal of Material and Performance, 1999,8(4): 443-449
[30] Weissman, S L, Sackman J, Harvey J T,et al. Seledtion of Laboratory Test Specimen Dimension for Permanent Deformation of Aspalt Concrete Pavements. Transportation Research Record 1681, 1999:113-120
[31] Fujie Zhou,Tom Scullion. DiscussiomThree Stages of Permanent Deformation Curve and Ruting Model. The Internationa] Journal of Pavement Engineering. Uol. 3(4). 2002, P251-260
[32] R.A.Tarefder,M.Zaman,K,Hobason.A Laboratory and Statistical Evaluantion of Factors Affecting Rutting.The International journal of Pavement Engineering.Vol.4(1) March 2003, P59-68
[33] Kandhal, P S, R B Mallick. Effects of gradation on Rutting Potential of Dense Graded Asphalt Mixtures. TRB, No 1767, 2001, P146-151
[34] Elie Y Hajj, Raj V Siddliartlian, et al. Development of Laboratory Based Uufied Permanent Deformation Model of HMA Mixture [C]. 84th TRB Annual Meeting January 9-13, 2005
[35] Cluadc Villicrs ct al. Intcrprctationg of Transverse Profiles to Detemine the Source of Rutting within Asphalt Pavement system[C]. 84th TRB Annual Meeting January 9-13, 2005
[36] Jorge B. Sousa, Joseph Craus, Carl L. Monismith. Summary Report on Permanent Deformation in Asphalt Concrete (SHRP-A/IR-91 -104). Strategic Highway Research Program. National Research Council. Washington, D, C. 1991
[37] Griffith A A. The phenomena of rupture and flow in solids. Phil.Trans. Roy. Soc. 1921, A211 163
[38] Irwin G R. Fracture Dynamics in Fracturing of Metals. ASTM Cleveland, 1948
[39] Irwin G R. Analysis of Stresses and Strains near the end of a crack traversing a plane. J Appl Mech.1957,24:361
[40] Mushkelishivili N I. Some Basic Problems of the Mathematical Theory of Elasticity. Translated by J R M Radok Noordhoff, 1963
[41] Dugdale D S.Yielding of steel sheets containing slits. J Mech. Phys Solids. 1960, 8: 100-104
[42] Wells A A. Unstable crack propagation in metals: Cleavage and Fast Fracture, Crack Propagation Symposium, Cranfield, 1961
[43] Billby B A, Cottrell A H and Swinden K H. The Spread of plastic yield from a notch Proc. Roy Soc 1964,A272 304
[44] Rice J R. A path independent integral and the approximate analysis of strain concentration by nothces and cracks[J]. Appl Mech. 1968, 379-385
[45] Sih G C. A special theory of crack propagation in Mechanics of Fracture (G C Sih ed) Vol. 1 Noordhoff, 1973
[46] Kaplan M F. Crack propagation and the fracture of concrete. J Am. Concrete Inst. 1961, 58: 591-610
[47]Bazant ZP and Oh,B.H.Crack band theory for facture of concrete[J].Materials and Structures,1983,16(93):155～177
[48]胡庆安，程侠，邰卫华．金属材料断裂预测损伤破坏准则的应用．长安大学学报(自然科学版)：2007，27(4)：100～102
[49]李雪红，徐洪钟，顾冲时．水工混凝土结构裂缝的稳定性分析．南京工业大学学报：2007，29(3)：20～24
[50]Jayatilaka des Ayal.Fracture of Engineering Brittle Materials[M].England,1979
[51]Elin A.Jensen,Will Hansen.Fracture Energy Test for Highway Concrete.Transportation Research Record 1730 Paper No.00-0937
[52]R.L.Krans,E.Tolman,M.F.C.Van De Ven.Semi-circular bending test:a practical crack growth test using asphalt concrete cores.Reflective Cracking in Pavements.Edited by L.Francken,E,Beuving and A.A.A.Molenaar.(?)1996 RILEM.Published by E & FN Spon,2-6 Bounary Row,London,SEI 8HN.ISBN 0 419 22260 X
[53]E.K.Tschegg,S.E.Tschegg-stanzl,J.Litzka.Fracture behaviour and bond strength of bituminous layers.Reflective Cracking in Pavements.Edited by L.Francken,E,Beuving and A.A.A.Molenaar.(?)1996 RILEM.Published by E & FN Spon,2-6 Bounary Row,London,SEI 8HN.ISBN 0 419 22260 X
[54]Mihai O.Marasteanu,Xue Li,Joseph E Labuz.Cracking in Pavements-Mitigation Risk Assessment and Prevention,5th International RILEM Conference,Limoges,France,5-7 May 2004
[55]J.M.Read.New Method for Measuring Crack Propagation in Asphalt Concrete[J].International Journal for Pavement Engineering.Vol:1 No.1 pp 15-35.2000
[56]K.W.Kim,H.M.E Hussein.Effect of Differential Contraction on Fracture Tougness of Asphalt Material at Low Temperatures[J].AAPT.1995
[57]Zhiwang Zhang,Reynaldo Roque,and Bjorn Birgisson.Evalution of Laboratory-Measured Crack Growth Rate for Asphalt Mixtures.Transportation Research Record 1767 paper No.01-0272.2001
[58]Aysar NAJD、郑传超．测量加筋沥青混凝土内的裂缝扩展(英文)．Journal of Southeast University(东南大学学报：英文版)2005．21(3)：342-347
[59]Aysar NAJD、郑传超、郭进英．纤维加筋沥青混凝土断裂性能试验．长安大学学报：自然科学版—2005．25(3)：28-32
[60]Aysar NAJD、郑传超．利用玻璃纤维增加沥青混凝土的断裂潜能研究．西安工业学院学报，2005年第02期：169-173
[61]张登良．半刚性基层沥青路面地断裂力学计算方法及其应用．中国公路学报，1998．11(2)：30-38
[62]孙立军．复合路面荷载型反射裂缝的力学分析和试验路验证．土木工程学报，2005．35(1)：50-56
[63]彭妙娟、程玉民．西三线沥青路面的荷载应力和温度应力分析．西安理工大学学报，1998年第二期
[64]杨春风．基层含裂缝沥青路面的应力分析．黑龙江工程学院学报．2003．17(3)：9-11
[65]杨春风．半刚性基层沥青路面温缩裂缝的有限元分析．桂林工学院学报．2004．24(1)：52-54
[66]毛成、邱延峻、李云鹏沥青路面表面裂纹扩展模拟及影响因素分析．西南交通大学学报．2004．39(4)：437-441
[67]杨春风．断裂力学理论在道路疲劳寿命预测中的应用．昆明理工大学学报．2003．28(6)：87-90
[68]贾艳东、宋玉普、黄志强．测定混凝土断裂参数试验方法的研究．低温建筑技术．2004(2)：11-13
[69]曾梦澜、马正军、易昕．广义Paris公式预测沥青路面的疲劳寿命．湖南大学学报(自然科学版)，2005年06期
[70]Seo Y,Kim YR,Schapery RA,Witczak MW,Bonaquist R.A study of crack-tip deformation and crack growth in asphalt concrete using fracture mechanics.Journal of the Association of Asphalt Paving Technologists.Volume:73 Conference Title:Technical Sessions of the Journal of the Association of Asphalt Paving Technologists.2004 Proceedings.Location:Baton Rouge,Louisiana
[71]Brooker T,Foulkers MD,Kennedy CK.Influence of mix design on reflection cracking growth rates through asphalt surfacing.Sixth international conference,structural design of asphalt pavements,volume I,proceedings,university of michigan,july 13-17,1987,ANN ARBOR,Michigan
[72]Majidzadeh K,Kauffmann EM,Chang CW.Verification of fracture mechanics concepts to predictcracking of flexible pavements
[73]Majidzadeh Kamran,Kauffmann E.M,Saraf C.L.Analysis of fatigue of paving mixtures from the fracture mechanics viewpoint
[74]F.Durbin(1974),Numerical inversion of Laplace transforms:an efficient improvement to Dubner and Abate's method[J],The Computer Journal,V.17.No.4,pp.371-376
[75]Dubner,R.,and Abate,J.(1968).Numerical inversion of Laplace transforms by relating them to the finite Fourier Cosine transform,J.ACM,Vol.15,No.1,pp.115-123
[76]S.Crump,Numerical inversion of Laplace transforms using a Fourier series approximation,JACM.,23(1976),89-96
[77]M.K.Miller and T.W.Guy,Numerical inversion of the Laplace transform by use of Jacobi polynomisls,SIAM Journal of Numerical Analysis,Vol.,3,624-635(1966)
[78]Davis,B 和 Martin,B.,Numerical Inversion of the Laplace Transform:ASurvey and Comparison of Methods,J.Comput.Phys.33(1979),1-32
[79]戴煜．Laplace变换的代数数值反演方法．数值计算与计算机应用．2001，No．4，281-285
[80]单华宁．Laplace变换的数值反演方法的研究．数值计算与计算机应用．1999，No．3：231-236
[81]谢咏梅，胡娟，单华宁，王国清．Laplace变换的数值反演算法的研究．南京师大学报(自然科学版)．Vol．24，No．4(2001)：12-15
[82]范天佑．断裂理论基础．科学出版社．2002年，北京
[83]郑传超．道路结构断裂力学基础[M]．西安：西北工业大学出版社．1997年11月。
[84]陈小庭，孙立军，李峰．长寿命沥青混凝土路面结构特点与设计研究．公路．2005年8月，第8期
[85]JTJ 014-97．沥青路面设计规范[S]．北京：人民交通出版社
[86]邓学钧．路基路面工程[M]．北京：人民交通出版社．2000
[87]徐世法．高等级道路沥青路面车辙的预估控制与防治．同济大学博士学位论文．1991．12
[88]任瑞波，谭忆秋，钟岱辉．沥青路面粘弹性问题的理论分析．四川建筑科学研究．第30卷，第1期，2004年3月
[89]任瑞波，钟阳，张肖宁，郭大智．多层粘弹性半空间地基对称问题的理论解．哈尔滨建筑大学学报．第33卷，第6期，2000年12月
[90]钟阳，陈静云，王龙，李玉华．求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法．计算力学学报．第20卷，第6期，2003年12月
[91]郑健龙，关宏信．温缩型反射裂缝的热粘弹性有限元分析．中国公路学报．第14卷，第3期，2001年7月
[92]任瑞波，谭忆秋，张肖宁．FWD动荷载作用下沥青路面层状体系粘弹解与弹性解分析．哈尔滨建筑大学学报．第34卷，第5期，2001年10月
[93]R.L.Krans et al.Semi-circular bending test:a practical cracks growth test using asphalt concrete cores
[94]R.L Krans,F.Tohnan and M.F.C.Van De Ven.Semi-Circular Bending test Using Core.[C]The Third International Conference on Reflective Cracking in Pavement,Maastricht,The Netherlands.1996
[95]Ye Guozheng.Fatigue Shear and Fracture Behavior of Rubber Bituminous Pavement[C].Third International Conference on Reflective Cracking in Pavements.1996
[96]沙庆林．高等级公路半刚性基层沥青路面[M]．北京：人民交通出版社．1999
[97]郝培文等．沥青混合料低温抗裂性能评价指标．西安公路交通大学学报，第20卷，第3期．2000
[98]F.J.Zhou and Sun Lijun.Lab Asphalt Testing Evaluation of Reflective Cracking[C].Accelerated Pavement Testing International Conference,Reno,Nevada 1999
[99]F.J.Zhou.Anti-Reflective Cracking Measures and Mechanistic Analysis[D].Ph.D.Dissertation,Tongji University.1998
[100]周志刚，张起森．加筋材料阻止沥青路面反射裂缝的桥联增韧的有限元分析．土木工程学报．Vol．33(1)：93-99(2000)
[101]易志坚，吴国雄．基于断裂力学原理的水泥混凝土路面破坏过程分析及路而设计新构想．重庆交通学院学报．Vol．2(1)：1—5(2001)
[102]罗睿，黄晓明．利用权函数计算沥青路面层间部分约束的面层底裂缝应力强度因子．岩土工程学报．Vol．23(5)：610-613(2001)
[103]才华，张敏江．反射裂缝的断裂及疲劳分析和模拟计算．沈阳建筑工程学院学报．Vol．13(3)：252-258(1997)
[104]冯建亚．沥青混凝土罩面层的开裂破坏规律分析．硕士毕业论文．大连理工大学，2002
[105]焦新海，周行春．半刚性路面反射裂缝防治措施研究综述．重庆交通学院学报．Vol．17(1)：52-57(1998)
[106]郑健龙，张起森．半刚性路面反射裂缝及其应力强度因子的有限元分析．岩土工程学报．1990，12(3)：22-26
[107]罗睿，黄晓明．沥青路面表面裂缝应力强度因子计算方法研究．公路交通科技，2002，19(1)：13-15
[108]彭妙娟，张登良，夏永旭．半刚性基层沥青路面的断裂力学计算方法及其应用．中国公路学报．1998，11(2)：30-38
[109]刘益河，张起森．用热光弹法研究路面裂缝稳定性问题．实验力学，1992，7(4)：364-370
[110]刘益河，张起森．用温度光弹法确定路面结构裂缝的应力强度因子．长沙交通学院学报．1991，7(1)．71-80
[111]M.A.Caltabianl and J.M.Brunton.Reflection Cracking in Asphalt Concrete[J].A.A.P.T,Vol 60,pp310-3320.1991
[112]Majidzadeh.Improved Methods to Eliminate Reflection Cracking,Report FHWA/RD-86/07,Washington,D.C.1985
[113]C.L.Monismith.Reflection Cracking:Analysis,Laboratory Studies,and Design Consideration[J].AAPT,Vol.49.1980
[114]S.J.Sulaiman,A.F.Stock.The Use of Fracutre Mechanics for The Evaluation of Asphalt Mixes.[C].AAPT.1995
[115]M.M.Jacobs,P.C.Hopman,A.A.A.Moleneer.Application of Fracture Mechanics Principle to Analyze Cracking in Asphalt Concrete[J].AAPT,Vol 65,1996
[116]Fatigue Response of Asphalt Aggregate Mixes Asphalt Research Program.Institute of Transportation Studies,SHRP,National Research Council,University of California,Berkeley,Washington,66 DC 1994
[117]Yoon-Ho Cho,Chiu Liu,Terry Dossey,et al.Asphalt Overlay Design Methods for Rigid Pavements Considering Rutting,Reflection Cracking and Fatigue Cracking Research Report 987-9,Center for Transportation Research Bureau of Engineering Research.University of Texas,Austun.1998
[118]R.A.A.Schapery.Theory of Crack Growth in Visco-Elastic Media,Report MM 2764-73-1,Mechanics and Materials Research Centre,Texas&M University,Texas.1973
[119]A.A.A Molenaar and Snods.Design Methods for Plain and Geogrid Reinforced Overlay[C].The third International Conference on Reflective Cracking in Pavements.1996
[120]A.Scarpas.Finite Elements Modeling of Cracking in Pavements[C].Third International Conference on Reflective Cracking in Pavements,Maastricht,The Netherlands.1996
[121]A.Scarpas,Blaauwendraad J,A.H.De Bondt and A.A.A.Molenaar.CAPA:A Modern Tool for The Analysis and Design of Pavements.[C].Second International RILEM Conference on Reflective Cracking in Pavements,Liege.1993
[122]张妍．沥青混凝土路面病害与加铺层的力学分析．长安大学硕士学位论文．2005年5月
[123]陈玉，沥青路面低温缩裂分析．长安大学硕士论文．2006年5月
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |